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Multispecies Stock-Assessment (MSM) and Bioenergetic Modeling

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figure 1,see caption
Figure 1.  Weight-dependent annual ration estimates for walleye pollock, Pacific cod, and arrowtooth flounder from the eastern Bering Sea.  Shaded polygons represent field-based rations estimated from three different methods: Mean. stomach Wt. (i.e., no correction; light gray), Beaudreau & Essington (digestion correction using prey condition; medium gray); Elliott & Presson (digestion correction using mean stomach weights; dark gray).  The thin line shows values reported in Livingston et al. 1986.  The remaining lines represent bioenergetic based estimates of consumption from the Wisconsin model (dotted line), the generalized von Bertalanffy growth equation (solid thick line) and the specialized von Bertalanffy (dashed line).

Multispecies Stock-Assessment Modeling (MSM) is a three-species model of some of the most productive fish stocks and key predators in the Bering Sea walleye pollock, Pacific cod, and arrowtooth flounder. Their biological interactions may influence natural mortality estimates and subsequent harvest recommendations. Thus MSM is a first-cut approach for implementing ecosystem-based management of fisheries resources in the Bering Sea.

MSM combines traditional catch-at-age stock assessment models with multispecies virtual population analysis models (MSVPA) in a statistical framework and uses abundance and diet data to estimate fishing mortality, recruitment, stock size, and predation mortality. MSM typically models the latter as a series of functional bioenergetics responses to derive temperature-dependent predator rations.

Because MSM can capture critical threshold effects that characterize many ecological interactions, such an approach also provides a statistical framework to evaluate and manage both the direct and indirect effects of fisheries harvest on multiple species. Additionally, we used projections of the model to derive biological reference points (BRPs) for various harvest control rule approaches under variable climatic conditions.

As part of the MSM modeling effort we have continued to update the bioenergetic parameters used in MSM. In particular, we recently completed a comparative analysis of field-based daily ration values (corrected for digestion) to bioenergetic-based ration estimates for the eastern Bering Sea (EBS), Gulf of Alaska (GOA), and Aleutian Islands (AI) regions for walleye pollock, Pacific cod, and arrowtooth flounder.

This comparative analysis is currently summarized in a draft manuscript tentatively titled "Field- and bioenergetic-based daily ration estimates for walleye pollock (Theragra chalcogramma), Pacific cod (Gadus macrocephalus), and arrowtooth flounder (Atheresthes stomias) from Alaska (USA)."

For this we refit Wisconsin bioenergetic parameters to published consumption data for the three (or similar) species and compared bioenergetic rations to digestion corrected field-based ration estimates (using two different methods) and von Bertalanffy derived estimates of consumption (Fig. 1). This allowed us to derive consumption parameters that can now be used to update regional MSM models.

figure 2,see caption
Figure 2.  Length-based prey selectivity for cannibalistic walleye pollock predators consuming walleye pollock prey of various sizes (shaded squares), and model estimates of selectivity (contour lines).  The horizontal and vertical bar graphs represent the row (i.e., suitability) or column (i.e., proportion of diet by weight) totals, respectively; solid lines represented foraging model estimates.

Additionally we have conducted a detailed analysis of allometric patterns in predation risk and prey selectivity (Fig. 2). These analyses have allowed us to parameterize the size-based foraging model used in MSM.

figure 3,see caption
Figure 3.  MSM estimates of spawning biomass of walleye pollock from the eastern Bering sea (blue line) and projections of unfished and 40% unfished biomass from MSM (solid and dashed blue lines, respectively), Ecosim (orange lines), and the 2011 stock assessment (horizontal gray bar).

We have applied the updated bioenergetic and foraging model parameters to the MSM model for the EBS. In particular, we have generated projections for the three species under various target harvest rates including (i) no fishing, and (ii) fishing to 40% of the unfished spawning biomass. Model predictions were compared to single species assessments from 2011 as well as Ecosim predictions for the Bering sea (Fig. 3).

We now are in the processes of generalizing the MSM model code to accommodate additional species, initially anticipated to include Steller sea lions and Bering Sea flatfish species.

The updated model and initial model results are being compiled in a draft manuscript titled "Incorporating bioenergetics into multi-species statistical catch-at-age models: an example from the Bering Sea."

By Kirstin Holsman, Kerim Aydin, Jim Ianelli

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